Higher Sobolev regularity of convex integration solutions in elasticity
In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically linearized model case, the hexagonal-to-rhombic phase transformation, we prove the existence of convex integration solutions $u...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
8 Oct 2016
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| In: |
Arxiv
Year: 2016, Pages: 1-69 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1610.02529
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| Author Notes: | Angkana Rüland, Christian Zillinger, and Barbara Zwicknagl |
| Summary: | In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically linearized model case, the hexagonal-to-rhombic phase transformation, we prove the existence of convex integration solutions $u$ with higher Sobolev regularity, i.e. there exists $\theta_0>0$ such that $\nabla u \in W^{s,p}_{loc}(\mathbb{R}^2)\cap L^{\infty}(\mathbb{R}^2)$ for $s\in(0,1)$, $p\in(1,\infty)$ with $0<sp < \theta_0$. We also recall a construction, which shows that in situations with additional symmetry much better regularity properties hold. |
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| Item Description: | Gesehen am 27.05.2021 |
| Physical Description: | Online Resource |